Student X--need to apply for a second entry

Hello! I am going to China next week to study medicine at a hospital i Fuzhou for 5 weeks. We applied for "double entry" but only got 1 entry back on our passports. The third week of our stay we have one "free week" to travel in Asia. So we need to apply for a second entry so we can come back and have our last 2 weeks at the hospital. We have heard that it's possible to apply for a second entry at local authorities when we get to China. Is that possible?
Thank you